Warning

If a function f(x) takes the form or ∞/∞ at x = a, then we say that f(x) is indeterminate at x = a.Other indeterminate forms: ∞ – ∞, 0 x ∞, 1∞, 00 and ∞0

L' Hospital's Rule

If f(x) and g(x) are functions of x such that f(a) = 0 and g(a) = 0, then where f '(x) and g '(x) are derivatives of f(x) and g(x) respectively.Note that differentiation (or derivatives of functions) is covered later which is a pre-requisite to L' Hospital's Rule. Yet evaluation of limits using differentiation formulae is dealt with here.

Note: While applying L' Hospital's Rule, we should differentiate the numerator and denominator separately. (We should not differentiate by the rule for finding the differential coefficient of the quotient of two functions). Before applying this rule, ensure that f(x) is of the form . Continue differentiation till you get a definite limit.

For other indeterminate forms, we should use expansions of various functions or apply algebra of limits.